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  \;

  <doc-data|<doc-title|Ludic Computing coursework<next-line>Experiments with
  Steering Behaviours in \ \ \ \ \ \ \ \ Processing>||<doc-author-data|<author-name|Paul
  Bonaud, Marcos Mainar Lalmolda>|<\author-address>
    \;
  </author-address>>|<doc-date|<date|>>>

  <section|Seek and Arrive>

  <subsection|Experiment 1.1>

  \;

  The mass of the agent together with its maximum force influence the
  distance in which the agent overshoots its target. The heavier the agent
  is, the more likely it is to have inertia and overshoot the target. The
  smaller the maximum force is, the less likely it is to head back towards
  the target during the overshoot. The maximum speed trivially influences the
  speed with which the agent heads towards the target. But also influences
  the inertia of the agent.

  <subsection|Experiment 1.2>

  \;

  The stopping distance will differentiate the Arrive from the Seek
  behaviour. Indeed if the stopping distance is very small, then the two
  behaviours will be the same. However, when the stopping distance is long
  enough, we can clearly see how the agent with the arrive steering behaviour
  slows down when approaching the target. By consequence it doesn't ``beat
  around the bush'' as much as the other one.

  <new-page>

  <section|Wander>

  <subsection|Experiment 2>

  <subsubsection|Method>

  \;

  In order to run a proper visual experiment on the wander behaviour we
  changed the boundaries (dead-stop) of the map to a wrapped map. This gave
  the agent the possibility to wander around in an ``infinite'' space with no
  screen limits. We could then change the 3 parameters of the steering
  behaviour and investigate their effects without having the agent to stop
  against walls.

  This was easily implemented as the wander behaviour has no real target (and
  so no wrapped distance calculation). We only had to change to agent's
  position in the <with|font-shape|italic|update()> method of the
  <with|font-shape|italic|Agent> class.

  <subsubsection|Result>

  \;

  The wander circle (i.e. both wander radius and distance parameters)
  influence the cone space in which the agent's direction is able to span.
  Therefore the narrower the cone is (i.e. big distance and small wander
  radius) the straighter it is to move. And the wider the cone is (i.e. small
  distance and big wander radius) the more likely the agent is to change
  direction.

  It is interesting to note that when the wander circle overlaps the agent
  (i.e. the agent is within the wander circle) the direction is not bounded
  anymore. Then the direction can be anywhere around the agent.

  Finally the jitter parameter gives the jittering with which the random
  target is generated. The bigger it is the more ``noise'' it will create and
  the target will flick around the wander perimeter. Thus the directions
  created on <with|font-shape|italic|update()> will flicker a lot. Whereas
  with a small jitter value, the agent's direction change in time will be
  smaller and the agent will keep more or less the same line/curve.

  \;

  To sum up here are 3 different wandering behaviours with a 10px radius
  agent which are interesting to observe. Paremeters with screenshots with
  cone drawn in yellow-orange and a black line to show the direction taken by
  agent.

  <\itemize-minus>
    <item><underline|Fairly straight>: distance = 100, wander radius = 5,
    jitter = 20

    or distance \<gtr\> 1, wander radius = 50, jitter = 2

    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|png>|*5/8|*5/8||||>

    <item><underline|Lost agent (staying at arount the same place and looking
    everywhere wround):>\ 

    distance = 1, wander radius = 20, jitter = 40

    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|png>|*5/8|*5/8||||>

    <item><underline|``Nice looking'' behaviour with a majority of curves:>

    distance = 100, wander radius = 60, jitter = 30

    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  </itemize-minus>

  <new-page>

  <section|Pursue and Evade>

  <subsection|Implementation>

  \;

  For this section, we first implemented the Flee behaviour based on Seek
  which had been implemented before. It only required a small change as Flee
  is only seeking to the opposite direction where the target is. Then we
  implemented the two new behaviours required: pursue and evade. The main
  difference between this sketch and the previous ones is that now we are
  heading for a moving target. Therefore, as seen in lectures, it is better
  to aim for where the target is heading rather than where it is right now.
  Thus, both new behaviours are based on predicting where the target is
  headi<em|>ng. We were required to use the time to target formula for
  calculating the amount of time to look ahead (<math|t<rsub|p*r*e*d>>) to
  predict the target's movement. Once <math|t<rsub|p*r*e*d>> is calculated
  then we calculate the predicted position of the target,
  <math|q<rsub|p*r*e*d>>. After experimentation, \ we decided to set
  <math|t<rsub|l*i*m>> to 5, which is a value long enough for the hunter to
  catch the prey according to our simulation parameters. We have to keep in
  mind that the predicted target position is only an estimation that has some
  assumptions behind: the target doesn't move (which we definitely know is
  false), the agent's speed doesn't change and the agent heads directly in a
  straight line to the target. Each time the <em|draw()> method is called by
  the Processing API (<em|<em|<verbatim|<em|frameRate<strong|<em|>>>>>>
  internal parameter), it will update the agents' positions and calculate a
  new estimation of the predicted position of the target,
  <math|q<rsub|p*r*e*d>>. Therefore, it is periodically correcting its
  estimation.

  To be able to differentiate better when reading the code, we created two
  specialised classes: <with|font-shape|italic|HunterAgent> and
  <with|font-shape|italic|PreyAgent> which inherit from the base class
  <em|Agent>. We added a field called <with|font-shape|italic|behaviour> in
  both of them and a getter and setter method to obtain and set the behaviour
  for the hunter and prey. This method is called from the
  <with|font-shape|italic|HuntDemo.pde> class file.

  One problem to handle in this section was to decide what to do when the
  prey gets to the edges or limits of the screen. We had various
  possibilities: stop the prey as if it had crashed against a wall, restart
  the simulation, bounce or wrap around the limits of the screen. For this
  particular section, we decided to stop the prey for simplicity and in the
  next sketch (Game of Tag) we would wrap around the limits of the screen and
  adapt the behaviours to make the game nicer.

  Finally, when the behaviour is pursue or evade, we allow the user to change
  the constant parameter, <em|k>, which multiplies <math|t<rsub|p*r*e*d>>.

  <subsection|Experiment 3>

  <subsubsection|Method>

  \;

  In order to perform this experiment, we ran 100 simulations for each pair
  of behaviours. In each simulation, we first measured the current time in
  the system using the <with|font-shape|italic|System.currentTimeMillis>
  method call. Then, in the hunting behaviours, seek and pursue, we check
  whether the hunter has captured the prey inside the
  <with|font-shape|italic|calculateRawForce> function. When the agent's
  centre is over the target then it means that the hunter caught the prey. We
  therefore call the <with|font-shape|italic|noLoop()> Processing API
  function in order to stop Processing from continuously executing the code
  in <with|font-shape|italic|draw()>. We then call our own method
  <with|font-shape|italic|restartDemo()> to get the current time (again using
  <with|font-shape|italic|System.currentTimeMillis>), get the difference
  between the previously saved start time of the simulation and write the
  capture time (in seconds) to a external file. Then we restart the
  parameters for the demo, placing the hunter and agents in random positions
  within the screen limits, getting the new current time for the new
  simulation start time, incrementing the simulation number and checking
  whether we have reached the 100 simulation limit we set. Notice that the
  external file is created at the beginning during the execution of the
  <with|font-shape|italic|setup()> initialisation method. While it is
  possible for the user to change the behaviour for both the prey and hunter
  agents, while performing the simulations the behaviours should be the same
  to get our desired data.

  As indicated in the experiment, we set the parameters of both agents so
  that they are identical in mass (10) and maximum force (15) but the hunter
  has a slightly higher maximum speed (8 vs 6). Both the hunter and the prey
  have a radius of 10.

  One problem we could early identify is that when the prey has 'intelligent'
  steering behaviour, i.e. it is using the evade behaviour to flee away from
  where the hunter thinks it is going to move after, and the hunter is using
  'non-intelligent' steering behaviour, i.e. seek, then it takes longer for
  the hunter to catch the prey given that they have very similar velocities
  and the same force and mass. As it can be observed sometimes, both agents
  run in loops, with the hunter running in circles trying to catch the prey
  and the prey evading it. The hunter approaches the prey constantly and in
  the end, as it is faster, it will reach it. If we increase the velocity of
  the hunter, they keep running in circles approaching their orbits more
  until the velocity is high enough and the hunter just catches the prey all
  the time. Therefore, to run the experiments, we had to set a time limit for
  the hunter to catch the prey. We decided to use a 5 seconds limit. If this
  amount of time elapses and the hunter hasn't still caught the prey, then we
  stop the current simulation and inform the user by printing a message on
  the standard output. The program will write more than 5 seconds in the
  output file and we know that this measure means the simulation had stopped
  because the hunter didn't manage to catch the prey within the time limit.
  When the hunter corners the prey to the limits of the screen then the prey
  isn't able to escape from it and it's soon caught within the time limit.

  When both agents have 'intelligent' steering behaviour, i.e. the hunter is
  using pursue and the prey is using evade we run into a similar situation.
  Both agents run in circles, with the hunter predicting the prey's position
  and the prey fleeing from where the hunter thinks it will go. As the
  hunter's velocity is slightly greater, in the end it will end catching the
  prey but again we limit the amount of time given to the hunter to catch the
  prey to 5 seconds.

  It is also worth mentioning that we didn't consider using the Arrive
  behaviour for pursue with the target's predicting position because this
  might allow the prey to escape while the hunter is reducing its speed when
  it is within the stopping distance.

  <subsubsection|Results>

  \;

  We generated 4 files, one for each pair of behaviours, with the measures of
  the capture times. The simulations where run with the following parameters:

  <\itemize-dot>
    <\itemize-dot>
      <item>Hunter mass = Prey mass = 10

      <item>Hunter max. force = Prey max. force = 15

      <item>Hunter max. speed = 8

      <item>Prey max. speed = 6

      <item>Hunter constant k in time to target formula = 1

      <item>Prey constant k in time to target formula = 1

      <item><with|mode|math|t<rsub|l*i*m> = 5 s>
    </itemize-dot>
  </itemize-dot>

  \;

  \ The files contain one capture time (in seconds) per line. We then copied
  and pasted the data in a spreadsheet (<em|data.ods>, submitted with the
  code) and calculated the mean capture times. The mean capture times follow:

  \;

  <\itemize-dot>
    <item>Seek vs Flee: 2.00852

    <item>Pursue vs Flee: 1.68416

    <item>Seek vs Evade: 2.12995

    <item>Pursue vs Evade: 2.27398

    \;
  </itemize-dot>

  <subsubsection|Conclusions>

  As we can observe, pursue vs flee slightly improves the time to capture the
  prey compared to seek vs flee. This is because pursue uses its calculated
  <math|t<rsub|p*r*e*d>> to estimate the time to the target while seek can be
  seen a special case with <math|t<rsub|p*r*e*d>> = 0, i.e. no prediction
  used. The differences aren't that big because the evader soon arrives to
  the walls and stops.\ 

  We can also observe that when the behaviours are seek vs evade then the
  prey is 'intelligent' while the hunter isn't predicting the target's future
  position. Therefore the hunter requires more time to catch the prey than in
  any of the two previous cases.

  When simulating pursue vs evade, both agents are predicting each other
  position and therefore they kind of cancel each other. As the hunter is
  slightly faster, it will catch the prey at the end but in many simulations
  it will reach the timeout limit to catch the prey as the behaviours are
  equivalent but going in opposite directions and their velocities are very
  similar. Therefore, it is reflected that it takes more time than before for
  the agent to catch the prey.

  <section|A Game of Tag>

  <subsection|Implementation>

  \;

  We started the implementation by combining the
  <with|font-shape|italic|WanderDemo> and <with|font-shape|italic|HuntDemo>.
  Compared to the ``static'' hard coded number of agents in the previous
  demos here we created a list of agents in the
  <with|font-shape|italic|TagDemo> that would act as the players of the game
  of tag. This was done to easily be able to add/change the number of players
  later.

  The major part of the game logic was then to be implemented in the
  <with|font-shape|italic|Agent> class. Thus we created a
  <with|font-shape|italic|Player> class extending the
  <with|font-shape|italic|Agent> and removed the two specialised agents
  (<with|font-shape|italic|HunterAgent> and PreyAgent).

  <subsubsection|Game logic>

  \;

  Like all previous experiments, we update the agents at each step of the
  rendering (in the <with|font-shape|italic|draw()> method). And on update of
  each player this is what we implemented:

  <\enumerate-roman>
    <item>Detect collision

    <item> <with|font-series|bold|if> 'it' has touched another player
    <with|font-series|bold|then> broadcast the new 'it' to everyone

    <item> <with|font-series|bold|if> the current player is 'it'
    <with|font-series|bold|then> find nearest player to seek

    <with|font-series|bold|else> flee away from 'it' or wander around

    <item> update force/velocity/position with
    <with|font-shape|italic|update()> method from superclass
    <with|font-shape|italic|Agent>
  </enumerate-roman>

  \;

  As a collision affects two players in a non commutative relation we don't
  need to check collision between <with|font-series|bold|each> player with
  <with|font-series|bold|all> others. But only from one player to the
  remainings to be processed. Thus when we process a
  <with|font-shape|italic|collisionDetection(..)> on one player, this player
  won't be checked for collision anymore until the end of the current step.

  \;

  <subsection|Problems encountered and how we solved them>

  \;

  In order to have a ``nice looking'' result we took into account the advices
  written on the cw statement. I.e. Players don't constantly run away
  (Players at good distance from 'it' wanders around rather than fleeing
  away) and when a player is caught they give a chance for the other to move
  away (by having a nill velocity).

  At first we didn't remove the screen boundaries like in
  the<with|font-shape|italic|WanderDemo>, and we were faced with a
  inconvenient behaviour when both the 'it' and the pursued agent were
  against a wall. Indeed they were getting stuck in the walls and just moving
  slowly along the walls. We then introduced the torus map in order to have a
  better view of the game. But this introduced a non realistic behaviour.
  I.e. the calculation of the distance between players was wrong when no
  boundaries was present. Thus every processing involving a distance
  calculation was wrong : the steering behaviours (wrong direction), nearest
  player calculation (wrong distance), and wander circle (wrong distance). So
  when the 'it' would try to catch a player and that this player wrapped
  around the other side of the map, the 'it' would stop pursuing him and find
  a new nearest target.

  \;

  This is why we introduced a <with|font-shape|italic|myDist(..)> static
  method in the <with|font-shape|italic|TagDemo> to be used in case of an
  absence of boundaries. And used it everywhere were needed.\ 

  <subsection|Results>

  \;

  We tried two major different settings to change the global behaviour of the
  game.

  \;

  Our first experiment was to use basic seek and flee behaviours with agent's
  <with|font-shape|italic|maxSpeed> randomly chosen from 5 to 15 to render a
  nice demo where the slowest agent becomes undoubtedly 'it'.

  \;

  The second was to add several behaviours for each players in order to add
  more randomness to the rendering. Adding fleeing and wandering behaviour to
  the fleeing agents enables 'it' to have a chance to catch another player
  easily when they all have the same speed.

  By adding random speed setting we end up in a fight between the slowest
  players with sometimes a fast player which gets touched by 'it' because of
  it's inertia.

  \;

  It was also nice to play around with 400+ players within the game.\ 

  With the settings of the first experiment and 600 players it is
  entertaining to see how a circle forms around 'it' which is roughly the
  wander circle limit. Here is a screenshot of the demo:

  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  \;

  With the settings of our second experiment and 400 players the results ends
  up in a big mess of players where 'it' changes very often. We added random
  radius for each players to create an even more messy looking result.

  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  <subsection|Conclusions>

  \;

  This coursework was well organised to end us playing around with settings
  and steering behaviours. Additionnaly to the challenge of coding we had the
  pleasure to see the rendering of changing settings and this was rewarding
  in each experiment. At the end of the tag of game implementation we could,
  with spare time, keep playing around by changing settings, adding
  interaction with the user (via keyboard) to control 'it', add more fantasy
  to the result (colours to players, 3D rendering..). But we found that our
  result obtained with 400+ players was a nice eye catching and entertaining
  rendering, just like a fireplace that you keep staring at.

  \;
</body>

<\initial>
  <\collection>
    <associate|language|american>
    <associate|par-hyphen|normal>
  </collection>
</initial>

<\references>
  <\collection>
    <associate|auto-1|<tuple|1|1>>
    <associate|auto-10|<tuple|3.2|4>>
    <associate|auto-11|<tuple|3.2.1|4>>
    <associate|auto-12|<tuple|3.2.2|5>>
    <associate|auto-13|<tuple|3.2.3|5>>
    <associate|auto-14|<tuple|4|5>>
    <associate|auto-15|<tuple|4.1|5>>
    <associate|auto-16|<tuple|4.1.1|6>>
    <associate|auto-17|<tuple|4.2|6>>
    <associate|auto-18|<tuple|4.3|6>>
    <associate|auto-19|<tuple|4.4|7>>
    <associate|auto-2|<tuple|1.1|1>>
    <associate|auto-3|<tuple|1.2|1>>
    <associate|auto-4|<tuple|2|2>>
    <associate|auto-5|<tuple|2.1|2>>
    <associate|auto-6|<tuple|2.1.1|2>>
    <associate|auto-7|<tuple|2.1.2|2>>
    <associate|auto-8|<tuple|3|3>>
    <associate|auto-9|<tuple|3.1|3>>
  </collection>
</references>

<\auxiliary>
  <\collection>
    <\associate|toc>
      <vspace*|1fn><with|font-series|<quote|bold>|math-font-series|<quote|bold>|1<space|2spc>Seek
      and Arrive> <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
      <no-break><pageref|auto-1><vspace|0.5fn>

      <with|par-left|<quote|1.5fn>|1.1<space|2spc>Experiment 1.1
      <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
      <no-break><pageref|auto-2>>

      <with|par-left|<quote|1.5fn>|1.2<space|2spc>Experiment 1.2
      <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
      <no-break><pageref|auto-3>>

      <vspace*|1fn><with|font-series|<quote|bold>|math-font-series|<quote|bold>|2<space|2spc>Wander>
      <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
      <no-break><pageref|auto-4><vspace|0.5fn>

      <with|par-left|<quote|1.5fn>|2.1<space|2spc>Experiment 2
      <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
      <no-break><pageref|auto-5>>

      <with|par-left|<quote|3fn>|2.1.1<space|2spc>Method
      <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
      <no-break><pageref|auto-6>>

      <with|par-left|<quote|3fn>|2.1.2<space|2spc>Result
      <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
      <no-break><pageref|auto-7>>

      <vspace*|1fn><with|font-series|<quote|bold>|math-font-series|<quote|bold>|3<space|2spc>Pursue
      and Evade> <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
      <no-break><pageref|auto-8><vspace|0.5fn>

      <with|par-left|<quote|1.5fn>|3.1<space|2spc>Implementation
      <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
      <no-break><pageref|auto-9>>

      <with|par-left|<quote|1.5fn>|3.2<space|2spc>Experiment 3
      <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
      <no-break><pageref|auto-10>>

      <with|par-left|<quote|3fn>|3.2.1<space|2spc>Method
      <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
      <no-break><pageref|auto-11>>

      <with|par-left|<quote|3fn>|3.2.2<space|2spc>Results
      <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
      <no-break><pageref|auto-12>>

      <with|par-left|<quote|3fn>|3.2.3<space|2spc>Conclusions
      <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
      <no-break><pageref|auto-13>>

      <vspace*|1fn><with|font-series|<quote|bold>|math-font-series|<quote|bold>|4<space|2spc>A
      Game of Tag> <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
      <no-break><pageref|auto-14><vspace|0.5fn>

      <with|par-left|<quote|1.5fn>|4.1<space|2spc>Implementation
      <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
      <no-break><pageref|auto-15>>

      <with|par-left|<quote|3fn>|4.1.1<space|2spc>Game logic
      <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
      <no-break><pageref|auto-16>>

      <with|par-left|<quote|1.5fn>|4.2<space|2spc>Problems encountered and
      how we solved them <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
      <no-break><pageref|auto-17>>

      <with|par-left|<quote|1.5fn>|4.3<space|2spc>Results
      <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
      <no-break><pageref|auto-18>>

      <with|par-left|<quote|1.5fn>|4.4<space|2spc>Conclusions
      <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
      <no-break><pageref|auto-19>>
    </associate>
  </collection>
</auxiliary>